| Projective Determinacy |
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| CATEGORIES ABOUT AXIOM OF PROJECTIVE DETERMINACY | |
| game theory | |
| descriptive set theory | |
| determinacy | |
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The axiom of projective determinacy, abbreviated '''PD''', states that for any two-player game of perfect information of length ω in which the players play Natural Number s, if the victory set (for either player, since the projective sets are closed under complementation) is projective, then one player or the other has a Winning Strategy . The axiom is undecidable in ZFC , unlike the full axiom of determinacy (AD), which contradicts the Axiom Of Choice . PD follows from certain Large Cardinal axioms, such as the existence of infinitely many Woodin Cardinal s. PD implies that all projective sets are Lebesgue Measurable (in fact, Universally Measurable ) and have the Perfect Set Property and the Property Of Baire . It also implies that every projective Binary Relation may be Uniformized by a projective set. REFERENCES |
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